HR: 0800h
AN: NG31B-0872    [Abstracts]
TI: Wavelet Domain Inversion Using Iteratively Reweighted Least Squares
AU: * Qu, L
EM: lqu@boisestate.edu
AF: Boise State University, 1910 University Dr., Boise, ID 83725 United States
AU: Routh, P
EM: routh@cgiss.boisestate.edu
AF: Boise State University, 1910 University Dr., Boise, ID 83725 United States
AB: We propose an approach for solving the discretized linear inverse problems in the wavelet domain. The solution minimizes the penalized least squares criterion with penalty being the level dependent $L_1$ norm of the Discreet Wavelet Transform of the discretized underlying signal. The solution of this mixed $L_2$ and $L_1$ norm minimization is non-linear. The non-linear solution in wavelet domain is sparse and is more appropriate for non-smooth signals. The numerical computation is carried out by iteratively reweighted least squares incorporating a line search acceleration. The proposed approach is compared with the classic regularization in extensive simulations. The tuning parameters are selected by data dependent methods including $L$-curve and cross validation.
DE: 3210 Modeling
DE: 3230 Numerical solutions
DE: 3260 Inverse theory
DE: 0644 Numerical methods
SC: Nonlinear Geophysics [NG]
MN: 2004 AGU Fall Meeting